project work for additional mathematics 2010 paper work 4

8/9/2019 PROJECT WORK FOR ADDITIONAL MATHEMATICS 2010 PAPER WORK 4

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PROJECT WORK FOR

ADDITIONAL

MATHEMATICS 2010

PAPER WORK 4

Statistics in Our Life

NAME: MUHAMADNASHRULHAKIMIE BIN KADIR

I/C NUMBER : 930421-03-6003

SCHOOL : SMK BAROHPIAL


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Contents

No Contents

1 Acknowledgement

2 Introduction

3 Part 1

4 Part 2

5 Part 3

6 Conclusion

7 Further Exploration

8 References


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Acknowledgement

First of all, I would like to say thank my teacher EN.Mohamad Noor Hisham bin

Muhamadwho had gave us some guides on how to complete this paperwork. Next to

my fellow teammates who had held on each other firmly until we had completed this

paperwork. Finally to my parents who had always encourage me to put in some effort to

complete such big task and also allowing me to visit each other's house to discuss about

this paperwork.

While I was conducting this paperwork, I have gained consciousness in many other

things in my life. Completing this paperwork in a team had gave me a chance to know

each other and broaden my view on Mathematics. I now know the correct way to apply

mathematic knowledge in my daily life to solve a lot of problems.

Besides that, I also have learnt to accept other ideas from different people to make out

all the possible results. Then, I know which is the best after those comparison made.

This way, I can save a part of time and materials needed to construct any of the objects.

For an example, a bridge construction. We use the same method to find out all the

things we needed to complete it in the most beautiful and cost saving way.


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Introduction

This project is carried out by every student who taking Additional Mathematic intheir SPM examination. This project carries such aims:-

y Apply and adapt a variety of problem solving strategies to solve routineand non-routine problems;

y Experience classroom environments which are challenging, interesting andmeaningful and hence improve their thinking skills.

y Experience classroom environments where knowledge and skills areapplied in meaningful ways in solving real-life problems

y Experience classroom environments where expressing ones mathematicalthinking,reasoning and communication are highly encouraged andexpected

y Experience classroom environments that stimulates and enhances effectivelearning.

y Acquire effective mathematical communication through oral andwriting,and to use the language of mathematics to express mathematicalideas correctly and precisely

y Enhance acquisition of mathematical knowledge and skills throughproblem-solving in ways that increase interest and confidence

y Prepare ourselves for the demand of our future undertakings and inworkplace


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Realise that mathematics is an important and powerful tool in solving real-life problems and hence develop positive attitude towards mathematics.

Train ourselves not only to be independent learners but also to collaborate,to cooperate, and to share knowledge in an engaging and healthy environment

Use technology especially the ICT appropriately and effectively

Train ourselves to appreciate the intrinsic values of mathematics and tobecome more creative and innovative

Realize the importance and the beauty of mathematics

We are expected to submit the project work within three weeks from the firstday the task is being administered to us.Failure to submit the written reportwill result in us not receiving certificate.


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History of Statistic

By the 18th century, the term "statistics" designated the systematiccollection of demographic and economic data by states. In the early 19th century,the meaning of "statistics" broadened, then including the discipline concerned withthe collection, summary, and analysis of data. Today statistics is widely employedin government, business, and all the sciences. Electronic computers haveexpedited statistical computation, and have allowed statisticians to develop"computer-intensive" methods.

The term "mathematical statistics" designates the mathematical theoriesof probability and statistical inference, which are used in statistical practice. Therelation between statistics and probability theory developed rather late, however.

In the 19th century, statistics increasingly used probability theory, whose initialresults were found in the17th and 18th centuries, particularly in the analysisof games of chance (gambling). By 1800, astronomy used probability models and

statistical theories, particularly the method of least squares, which was inventedby Legendreand Gauss. Early probability theory and statistics was systematized

and extended by Laplace; following Laplace, probability and statistics have beenin continual development. In the 19th century, social scientists used statisticalreasoning and probability models to advance the new sciences of experimental

psychology and sociology; physical scientists used statistical reasoning andprobability models to advance the new sciences of thermodynamics and statisticalmechanics. The development of statistical reasoning was closely associated withthe development of inductive logic and the scientific method.

Statistics is not a field of mathematics but an autonomous mathematical science,

like computer science or operations research. Unlike mathematics, statistics hadits origins in public administration and maintains a special concernwith demography and economics. Being concerned with the scientificmethod and inductive logic, statistical theory has close association withthe philosophy of science; with its emphasis on learning from data and making best

predictions, statistics has great overlap with the decision


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science and microeconomics. With its concerns with data, statistics has overlapwith information science and computer science.

How about statistic today?

During the 20th century, the creation of precise instruments for agriculturalresearch, public health concerns (epidemiology, biostatistics, etc.),industrial quality control, and economic and social purposes(unemployment rate, economy, etc.) necessitated substantial advances in

statistical practices.

Today the use of statistics has broadened far beyond its origins. Individualsand organizations use statistics to understand data and make informeddecisions throughout the natural and social sciences, medicine, business, andother areas.

Statistics is generally regarded not as a subfield of mathematics but rather asa distinct, albeit allied, field. Many universities maintain separatemathematics and statistics departments. Statistics is also taught indepartments as diverse as psychology, education, and public health.


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Part 1

The prices of goods sold in shops vary from one shop to another. Shoppers tend tobuy goods which are not only reasonably priced but also give value for theirmoney.

You are required to carry out a survey on four different items based on thefollowing categories i.e. food, detergent and stationery. The survey should be donein three different shops.

a) Collect pictures, newspaper cuttings or photos on items that you havechosen. Design a collage to illustrate the chosen items

Answer:

Food

Self-raising flour


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Sugar

Eggs (Grade A)

Butter


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Detergent


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Stationery


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Question

(b) Record the items and their prices systematically as in Table 1. Since itemsmaybe differently packed, be sure to use consistent measurements for each item

selected so that comparison can be done easily and accurately.


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Answer:

Category Item Price(RM)Gui Brothers G-Mart Superstore

Food1.Self-Raising

Flour(1000g)4.00 3.70 3.60

2.Sugar(1000g) 2.00 1.90 1.803.Butter(250g) 4.70 4.50 4.30

4.Eggs(Grade A)1 dozen

5.90 5.50 5.00

Total Price 16.60 15.60 14.70

Detergent1.Soap(3 bars) 3.20 3.00 2.80

2.Liquiddishwasher(1000ml)

4.29 3.90 3.20

3.Clothesdetergent(3kg) 18.90 17.00 16.504.Toiletcleaner(500ml)

5.50 5.50 5.50

Total Price 31.89 29.40 28.00

Stationery1.Sharpener 1.50 1.30 1.002.Pencil(2B-1 dozen)

5.00 4.80 4.50

3.Pen 1.30 1.20 1.004.Eraser 1.30 1.20 1.10

Total Price 9.10 8.50 7.60Grand Total 57.59 53.50 50.30


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Question

(c) Create at least two suitable graphical representations (the use of ICT is

encouraged) to compare and contrast the price of the items chosen.

Answer:

1)


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2)


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3)


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Question

(d) Based on the graphical representation that you have constructed in Part 1(c),interpret, discuss and draw conclusions. Comments on your findings.

Answer:

Based on the graphical representations that I have constructed in Part 1(c), it isshown that there are large and small differences among the prices of items in eachcategory between the shops. In the food category, the smallest price differences areof those of sugar, while the highest is the price of eggs. Besides food, detergentalso shows a large price difference between its items. Among them is the price of

liquid dishwasher and clothes detergent. On the other hand, stationery itemdoesnt have any obvious price difference. The graph also show that most of theitems that are high priced comes from the Gui Brothers Supermarket, while thelowest price items come from the Discount Store. The graph 1(d) will show theconclusion of the difference among the shops based upon the shops grand total.


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Graph 1(d)


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Question

(e) Identify an item that has a large price difference among the shops.

Calculate the mean and standard deviation of that particular item. Hence, suggestand discuss possible reasons for the price difference.

Answer:

Liquid dishwasher:

Mean=

=17.47Standard deviation

= ()/N ( )

=

- (17.47)

=0.97

The large price difference of clothes detergent among the shops maybe because ofthe standard of the shop.A high standard shop or supermarket, the items soldintend to be much more expensive than a regular shop or supermarket.Also, the

price difference of the items may also due to the quality of the item present. Abetter quality means a higher price.


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Part 2

Every year SMK Tengku Mahmud Iskandar organizes a carnival to raisefunds for the school. This year the school plans to install air conditioners inthe school library. Last year, during the carnival, your class made and soldbutter cakes. Because of the popularity of the butter cakes,your class hasdecided to carry out the same project for this years carnival.

Question

(a) Suggest a shop from Part 1 which you would go to purchase theingredients for the butter cakes.State and discuss your reasons for

purchasing from the shop you suggested.

Answer:

The Superstore.This is because the total price of the ingredients from thisshop is the lowest from the three shops.

Question

(b) Complete Table 2 with the prices of the items found in theshop/supermarket that you have chosen.

Answer:

Ingredient QuantityPer cake Price in the year2009(RM) Price in the year2010(RM)Self-raising flour 250g 0.90 0.90Sugar 200g 0.35 0.36Butter 250g 3.30 4.30E ggs(Grade A) 5 eggs (300g) 1.25 2.10


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Question

(i) Calculate the price index for each of the ingredients in Table 2 for theyear 2010 based on the year 2009

Answer:

1. Self-raising flour=

2. Sugar=

3. Butter=

Ingredient QuantityPer cake

Price in theyear

2009(RM)

Price in theyear

2010(RM)

Price index for theyear 2010 based on

the year 2009 ()

Self-raisingflour 250g 0.90 0.90 100

Sugar 200g 0.35 0.36 102.86Butter 250g 3.30 4.30 130.30Eggs(GradeA)

5 eggs(300g)

1.25 2.10 168


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4. Eggs(Grade A)=

Question(ii) Calculate the composite index for making a butter cake in the year 2010based on the year 2009. Discuss how you obtained your answers.

Answer:

To calculate the composite index, weightage is needed (W),

Ingredients Weightage (W)Self-raising flour

Sugar

Butter

Eggs(Grade A)

Composite index

=128.54


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Question

(iii) In the year 2009,the butter cake was sold at RM15.00 each.Suggest asuitable selling price for the butter cake in the year 2010.Give reasons for

your answer.Answer:

On 2009,RM 15.00

On 2010, price=

=

=19.30

Thus,the suitable price for the butter cake for the year 2010 is RM19.30.The

increase in price is also suitable because of the rise in the price of the ingredients.

Question

(c)(i) Find out from reliable sources how to determine suitable capacity of airconditioner to be installed based on the volume/size of a room.

Answer:

For common usage,air conditioner is rated according to horse power (1HP),which is approximately 700W to 1000W of electrical power. It is suitable for a

room size 1000ft which is around 27m of volume.


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Question

(ii) Work in groups to estimate the volume of your school library. Explain howyou arrive at your answer. Hence, determine the number of air conditioners with

the appropriate capacity required for your library.Answer:

By using a measuring tape,the dimension for the library is:

Height=3.6m

Width=9.17m

Length=20.12m

Volume of the room=3.69.1720.12

=664.20m

1 unit of air conditioner is for 27m

For 664.20m=

=24.6

That means our school library needs 25 unit of air conditioner.


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Question

(iii) If your class intends to sponsor one air conditioner for the school library,

how many butter cakes must your class sell in order to buy the air conditioner?

Answer:

1 unit of 1HP air conditioner=RM700

Cost for a cake =0.9+0.36+4.3+2.1 =7.66

Selling price =RM19.30

Profit =19.30-7.66

=RM11.64

Number of cakes to buy 1 unit of air conditioner =

= 60.13 = 60 cakes


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Part 3

As a committee member for the carnival, you are required to prepare an estimatedbudget to organize this years carnival. The committee has to take into theconsideration the increase in expenditure from the previous year due to inflation.The price of food, transportation and tents has increased by 15%. The cost of

games, prizes and decorations remains the same, whereas the cost ofmiscellaneous items has increase by 30%.

Question,

a) Complete Table 3 based on the information given above.Answer,

E xpenditure Amount in 2009(RM)

Amount in 2010(RM)

Food 1200.00 Games 500.00 500.00

Transportation 300.00 345.00 Decorations 200.00 Prizes 600.00 Tents 800.00 920.00

Miscellaneous 400.00 5

Table 3


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Question

b) Calculate the composite index for the estimated budget of the carnival in theyear 2010 based on the year 2009. Comment on your answer.

Solution.

E xpenditure Amount in2009(RM)

Amount in2010(RM)

Price Index, I

I=

Weightage,

W

Food 1200.00 1380.00 115 12Games 500.00 500.00 100 5Transportation 300.00 345.00 115 3

Decorations 200.00 200.00 100 2 Prizes 600.00 600.00 100 6Tents 800.00 920.00 115 8

Miscellaneous 400.00 520.00 130 4

Composite Index

=

=

= =111.625

The total price for the year 2010 increase by 11.625%. This is because some pricein the year 2009 increased in the year 2010.


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Question.

c) The change in the composite index for the estimate budget for the carnivalfrom the year 2009 to the year 2010 is the same as the change from the year2010 to the year 2011. Determine the composite index of the budget for the

year 2011 based on the year 2009.

Solution.

Composite index for the year 2009 to the year 2010

=111.625

Composite index for the year 2010 to the year 2011

=111.625

E

=E

E

E

=111.625111.625

E

124.60


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Further Exploration

Index numbers are being used in many different daily situations, for example

air pollution index, stock market index, gold index and property index.Obtain information from the internet or other reliable sources on the importanceof two different types of index number of your choice. Elaborate the use and theimportance of these index numbers in daily life.

Air Pollution Index

Air pollution is the introduction of chemicals, particulate matter, or biologicalmaterials that cause harm or discomfort to humans or other living organisms, ordamages the natural environment into the atmosphere.

The atmosphere is a complex dynamic natural gaseous system that is essentialto support life on planetEarth. Stratospheric ozone depletion due to air pollutionhas long been recognized as a threat to human health as well as to theEarth's ecosystems.

TheAir Quality Index(AQI) (also known as theAir Pollution Index(API)orPollutant Standard Index(PSI) is a number used by government agencies tocharacterize the quality of the air at a given location. As the AQI increases, anincreasingly large percentage of the population is likely to experience increasingly

severe adverse health effects. To compute the AQI requires an air pollutantconcentration from a monitor or model. The function used to convert from air

pollutant concentration to AQI varies by pollutant, and is different in differentcountries. Air quality index values are divided into ranges, and each range is

assigned a descriptor and a color code. Standardized public health advisories areassociated with each AQI range. An agency might also encourage members of the

public to take public transportation or work from home when AQI levels are high.


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Limitations of the AQI

Most air contaminants do not have an associated AQI. Many countriesmonitor ground-level ozone, particulates, sulphur dioxide, carbon

monoxide and nitrogen dioxide and calculate air quality indices for thesepollutants.

Causes of Poor AirQuality

The AQI can worsen (go up) due to lack of dilution of air emissions by fresh air.Stagnant air, often caused by an anticyclone or temperature inversion, or otherlack of winds lets air pollution remain in a local area.

Indices by location

South Korea

The Ministry ofEnvironment of South Korea uses the Comprehensice Air-qualityIndex (CAI) to describe the ambient air quality based on health risk of airpollution. The index aims to help the public easily understand air quality level and

protect the health of people from air pollution. - The CAI has values of 0 through500, which are divided into six categories. The higher the CAI value, the greaterthe level of air pollution. - Of values of the five air pollutants, the highest is theCAI value.


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CAI Description Health Implications

0-50 Good

A level that will not impact patients suffering from

diseases related to air pollution.

51-100

ModerateA level which may have a meager impact on patients incase of chronic exposure.

101-150

Unhealthy forsensitive groups

A level that may have harmful impacts on patients andmembers of sensitive groups.

151-250

Unhealthy

A level that may have harmful impacts on patients andmembers of sensitive groups (children, aged or weak

people), and also cause the general public unpleasantfeelings.

251-350

Very unhealthyA level which may have a serious impact on patients andmembers of sensitive groups in case of acute exposure.

351-500

HazardousA level which may need to take emergency measures forpatients and members of sensitive groups and haveharmful impacts on the general public.


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Malaysia

The air quality in Malaysia is reported as the API or Air Pollution Index. Four ofthe index's pollutant components (i.e., carbon monoxide, ozone, nitrogen dioxideand sulfur dioxide) are reported in PM10 particulate matter is reported in g/m.

Unlike the American AQI, the index number can exceed 500. Above 500, a state ofemergency is declared in the reporting area. Usually, this means that non-essential

government services are suspended, and all ports in the affected area closed.There may also be a prohibition on private sector commercial and industrialactivities in the reporting area excluding the food sector.


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Stock Market Index

A comparison of three major U.S. stock indices: theNASDAQ Composite, DowJones Industrial Average, andS&P 500. All three have the same height at March2007. Notice the large dot-com spike on the NASDAQ, a result of the large numberof tech. companies on that index.

A stock market indexis a method of measuring a section of the stock market.Many indices are cited by news or financial services firms and are usedas benchmarks, to measure the performance of portfolios such as mutual funds.

Types of indices

Stock market indices may be classed in many ways. A 'world' or 'global' stockmarket index includes (typically large) companies without regard for where theyare domiciled or traded. Two examples are MSCI World and S&P Global 100.

A national index represents the performance of the stock market of a givennation and by proxy, reflects investor sentiment on the state of its economy. Themost regularly quoted market indices are national indices composed of the stocksof large companies listed on a nation's largest stock exchanges, such as the

American S&P 500, the Japanese Nikkei 225, and the British FTSE100.

The concept may be extended well beyond an exchange. The Dow Jones TotalStock Market Index, as its name implies, represents the stocks of nearly every

publicly traded company in the United States, including all U.S. stocks traded on

the New York StockExchange (but not ADRs) and most traded onthe NASDAQ and American StockExchange. Russell Investment Group added tothe family of indices by launching the Russell Global Index.

More specialised indices exist tracking the performance of specific sectors of themarket. The Morgan Stanley Biotech Index, for example, consists of36 American firms in the biotechnology industry. Other indices may track


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companies of a certain size, a certain type of management, or even more specialized criteria one index published by Linux Weekly News tracks stocks ofcompanies that sell products and services based on the Linux operatingenvironment.

Index versions

Some indices, such as the S&P 500, have multiple versions.[1] These versions candiffer based on how the index components are weighted and on how dividends areaccounted for. For example, there are three versions of the S&P 500 index: pricereturn, which only considers the price of the components, total return, whichaccounts for dividend reinvestment, and net total return, which accounts for

dividend reinvestment after the deduction of a withholding tax. As anotherexample, the Wilshire 4500 and Wilshire 5000 indices have five versions each: fullcapitalization total return, full capitalization price, float-adjusted total return,

float-adjusted price, and equal weight. The difference between the fullcapitalization, float-adjusted, and equal weight versions is in how indexcomponents are weighted.

Uses and importance of air pollution index and stock market index

As everyone can see,the air pollution index is use by the government to measurethe air quality index and to detect any pollutants in our countrys air.This is toensure the air is clean and safe for us to inhale.Besides that,an early warning canbe given to us if the air pollution is to high for us to get out of our homes. Thiswarning is given based upon readings and interpretations of the air pollution

index.

As for the stock market index, it is mainly for the business entrepreneurs. This typeof index is used to determine the outcome of a stock market and also the conclusionof a stock market. The stock market index is important because a countryseconomical state sometimes depend on it.


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Conclusion

After doing research,answering questions,drawing graphs and some problemsolving, I saw that the usage of statistics is important in daily life.It is not justwidely used in markets but also in interpreting the condition of the

surrounding like the air or the water.Especially in conducting an air-pollutionsurvey.In conclusion,statistics is a daily life nessecities.Without it,surveyscant be conducted,the stock market cant be interpret and many more.So,we

should be thankful of the people who contribute in the idea of statistics.

project work for additional mathematics 2010 paper work 4

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